Machine Stress Rating (MSR) is a process by which the stress rating of dimension lumber is determined from a measurement of its stiffness, or Modulus of Elasticity (E). It is known from experimental work that a relationship exists between the bending stiffness of a piece of lumber, and its strength or Modulus of Rupture (MOR). Since the only way to determine MOR is to actually break the piece and measure the load required to break it, the next-best thing in machine stress rating is to measure stiffness, compute modulus of elasticity, and then predict modulus of rupture. Lumber sorted on the basis of E has been found to possess a very good correlation between MOR and grade, as opposed to practically no correlation between visual grade and the breaking strength, or MOR. Load ratings of visually-graded material have been drastically reduced because of the poor correlation between visual defects and the load-bearing capabilities of lumber.
Machine stress rating of dimension lumber has increased the accuracy of lumber grading and hence the efficient utilization of lumber resources. In North America the MSR process involves measuring the flatwise modulus of elasticity (E) of every piece of lumber, automatically spray marking each piece according to its E characteristics, and applying a grade mark according to grade rules. Background information on such testing processes and equipment can be found in U.S. Pat. Nos. 3,194,063 (McKean) and 3,196,672 (Keller).
The machine stress rating program for dimension lumber is now in place in many mills in western Canada, much of the United States, and in other major lumber producing countries of the world. In addition to testing each piece in the production line for flatwise E, a sample of production for each size, species, and grade combination from each shift is tested in edgewise bending for E and strength. In some cases, a tension proof load test is performed also. This off-line quality control program has been designed to assure that the lumber sold as MSR lumber meets the grade requirements for edgewise bending E and strength. In contrast, lumber sold under visual grade rules is not subject to any testing or quality control for structural properties.
Machine stress rating has become a mature concept. Producers know there is a marketplace for MSR lumber if they produce it, and users demanding structural performance know they can depend on a source of supply if they design to the structural values in MSR lumber. MSR lumber has become an attractive component of dimension lumber sales because there are economic incentives for both the producer and the user.
Knowledge of E from the MSR process as practiced today is important in its own right because it determines the deflection of lumber under a given load. It also determines the strength of lumber when it is used as a long thin column. Studies have shown that E can be used as a predictor of lumber bending and tensile strength, and its use in predicting strength accounts for about 50% of the variance of the strength.
A necessary part of the MSR process is to visually inspect each piece of material for defects which are not discernible in the bending stiffness test. It is necessary to down-grade material with excessively large edge-knots, for instance, since these defects have more detrimental effect on edgewise bending strength than is apparent in the flatwise bending measurement of stiffness. The flatwise bending stiffness test remains the best and most practical single method of predicting strength in use; and when the visual overrides are applied, the result is the best method known today to sort material for structural uses.
It is the objective of this disclosure to utilize grain angle measurements in addition to E measurements for lumber grading purposes and for the prediction of lumber strength, specifically the prediction of tensile strength of lumber.
The relationship of strength to grain angle in wood has been stated with a Hankinson formula as: EQU N=PQ/(P sin.sup.n .theta.+Q cos.sup.n .theta.) (1)
where N represents the strength at an angle .theta. from the fiber direction, Q is the strength across the grain and P is the strength parallel to the grain. The power n has been found to be in the range 1.5 to 2 and the ratio Q/P in the range of 0.04 to 0.07 for tensile strength.
A Hankinson relation for E has also been found to hold where N, Q, and P are E values at angle .theta., across and along the grain respectively. The power n is 2, and Q/P is in the range 0.04 to 0.12. Because the MSR process measures bending E, the prediction of strength depends indirectly on grain angle; consequently, there has been industry skepticism concerning whether direct measurement of grain angle would contribute additionally to strength prediction.
To properly understand the present disclosure, one must look at the distinction between "general grain angle" and "local grain angle" along a wooden board. General grain angle is defined here as the average grain angle over some length of lumber that is long with respect to the extent of knots or other local grain angle perturbations. Excessive general grain angle can be caused by spiral grain in trees, bowed logs, taper, poor sawing or simply the shape of the log before it was cut. Local grain angle is the grain angle defined on a smaller scale, and knots are the usual source of local grain angle problems.
Bending E measurements in production-line MSR equipment must necessarily be over a test span length, typically 900 to 1200 mm, that is long with respect to local grain angle deviations (to avoid significant contributions from compression perpendicular to grain at the lumber-roller interfaces). The effect of poor local grain angle is therefore partially masked by the measurement, which can be shown to be a weighed average of the localized E values along the length of the test span. Thus, it can be inferred that the MSR process accounts for the effect of general grain angle on strength, but does not account for the effect of local grain angle.
The relation between strength and local grain angle is not really conjecture, because experimental work performed over the years in refining the MSR process has shown the importance of visual edge knot determinations (and hence local grain angle) in properly qualifying dimension lumber for the higher MSR lumber grades. The problem, of course, is in being able to visually quantify the sizes and locations of knots and other grain perturbations over the full length of the lumber at production speeds. The fact that the visual graders do function admirably well in this environment is a tribute to their training and attentiveness.
Automated grain angle measurements have been possible since 1977, but the technique has yet to be implemented in the production line. The primary reason for this delay is that no one has demonstrated or presented to the industry a clear vision of how the grain angle data would be used to improve the lumber sorting process.
Details of an apparatus for measuring slope of grain (or grain angle) are disclosed in U.S. Pat. No. 3,805,156 (Norton et al.). The use of such equipment for measurement of geneal grain angle is discussed in an article titled "Measuring General Slope of Grain With the Slope-of-Grain Indicator" (Forest Products Journal, Vol. 34, No. 7/8, July/August 1984). Its application to measurement of local grain angle is the subject of an article titled "Measuring Localized Slope of Grain by Electrical Capacitance" (Forest Products Journal, Vol. 36, No. 10, October, 1986). The contents of these three publications are hereby incorporated by reference as part of the present disclosure.
Automating the evaluation of local grain angle and its effect on strength relieves the visual grader from having to make this determination, thus freeing the grader for making determinations of other important visual characteristics of the lumber. An automated measurement of grain angle would almost certainly be more accurate than a visual determination and would have the advantage of being the same over time, over different graders, and at different locations. Consequently, a more credible correlation between various types of local grain angle characteristics and lumber strength can be achieved.
"Grain angle," as used in this disclosure, is the direction of the projection of the wood fibers onto the measurement surface. While grain angle is physically measured about a surface of a board, the grain angle values will often be influenced by sub-surface wood grain patterns. The depth of such influence will be dependent upon the specific type of equipment used to measure grain angle, but it is to be understood that surface measurement of grain angle is not necessarily limited to surface wood grain characteristics.
FIG. 1 geometrically illustrates the angular relationship involved in local grain angle measurement. The measurement surface is a plane, which can be either a face F or an edge E of the lumber specimen S, recognizing that the face grain angle .theta..sub.f will usually be different from the edge grain angle .theta..sub.e. The zero grain angle reference is taken as a line on the measurement surface parallel to the longitudinal axis of the lumber in the z direction. Positive grain angle is measured counter-clockwise from the zero angle reference when looking at the lumber surface from the outside.
One can also define grain angle in three dimensions as a function of both face and edge grain angles so that it is the angle of the wood fibers relative to the longitudinal axis of the lumber. From FIG. 1, which illustrates grain angles .theta..sub.f and .theta..sub.e, the grain angle .theta..sub.a as measured from the axis can be stated as: EQU .theta..sub.a =tan.sup.-1 (tan.sup.2 .theta..sub.e +tan.sup.2 .theta..sub.f).sup.1/2 ( 2)
An excellent approximation for small angles .theta..sub.e and .theta..sub.f is: EQU .theta..sub.a =(.theta..sub.e.sup.2 +.theta..sub.f.sup.2).sup.1/2( 3)
The earliest commercial grain angle measuring equipment included circuitry for computing .theta..sub.a from the approximate formula. To simplify the present effort, attention shall be limited to the individual projections .theta..sub.e or .theta..sub.f. To simplify the notation of measured grain angle, it shall be referred to as .theta..
Grain angle measuring equipment of the type described in U.S. Pat. No. 3,805,156 utilizes the fact that the dielectric constant of wood is greater along the direction of the wood fibers than it is across the grain. It applies the concept of rotating capacitor plates at a uniform speed, where the capacitor plates are coplanar sectors of a circle with gaps between them and are arranged so that the wood becomes part of the dielectric medium. A radio frequency field is introduced to the capacitor plates; and a sinusoidal signal is created as the capacitor plates rotate, because the capacitance changes as the field is alternately directed along and then across the fibers. Phase measurement of the sinusoidal signal relative to a fixed reference signal yields a number which can be scaled and translated to obtain the grain angle. In present equipment, measurements are taken at the power-line frequency rate, i.e. at 50 or 60 measurements/second where each measurement is the average grain angle over the lumber area covered by the detector unit capacitor plates during the measurement interval.
Research efforts with grain angle measurements have concentrated primarily on general grain angle determinations. However, the capability of the measuring equipment to determine local grain angle has always been present, and its sensitivity to grain angle perturbations about knots has been known from the first. Existing publications that compare local grain angle measurements from a grain angle indicator with the actual grain angle on a closely spaced grid defined on the surface of a piece of lumber have clearly demonstrated the ability of existing equipment to measure local grain angle.
Several modifications and additions have improved the existing grain angle indicator. Recently, a computer controlled lumber transport mechanism has been developed which has allowed the instrument to be more useful in a laboratory environment. The transport mechanism holds the lumber and, by means of a cable chain attached to the lumber, uses a stepper motor to successively drive the lumber longitudinally over the grain angle indicator detector unit. After each pass of the lumber, another stepper motor causes the detector unit to more incrementally in the transverse direction of the lumber. While the lumber is moving longitudinally, the computer automatically reads and stores grain angle data. When the system has completely scanned the designated surface area of the lumber, the stored grain angle data can be viewed as an array of numbers, each representing the grain angle at a point on a grid previously defined by the operator.